This invention relates to the field of electronic design automation, and in particular, improved techniques for photolithography mask design.
Lithography mask optimization methods either force the mask to satisfy a priori mask manufacturability constraints at all times or use the “regularization” procedures of “inverse methods” to favor solutions that satisfy these constraints. More generally, there can be some constraints built into the mask representation or optimization algorithm and others handled through regularization procedures. Conceptually, an optimization algorithm can be more efficient in terms of speed and quality of solution by searching an unconstrained solution space, using regularization to guide the search to more desirable masks, than by searching in a heavily constrained space where one point may not be reachable from another in any straightforward way.
Many “inverse lithography” methods represent the mask using continuous tones that must be regularized to assume allowable mask values. For example, a chrome-on-glass mask can only have transmission values of one or zero. For this case, the usual simplistic regularization procedure is to add a term to the cost function that favors these values over others, and perhaps perform a threshold operation on the result to fully quantize the mask. By way of example, a term that could be used to accomplish this would be:U=16m2(1−m)2 
where m is the mask amplitude transmission value as a function of position and the total cost is obtained by integrating U over the mask area. This form of U has minima at m=0 and m=1, and a maximum of 1 at m=½. Unfortunately, if the term is given too much weight, the mask obtained will be close to a quantized mask but may not print well, and if it is given too little weight, it will not be sufficiently close to a quantized mask, and so will not print well after a threshold is applied. Worse still, there may not be any fixed term that will yield an acceptable mask.
The fundamental problem is that a sizeable area of low transmission value against a dark background may need to be represented by a narrow feature of full transmission value, which will require the solution to climb too big a hill in the regularization term. The opposite case can also occur, namely, where there is a sizeable area of somewhat less than full transmission within a fully transmitting region that needs to be represented as a narrow feature of zero value.
(Assuming there were no other mask criteria, one could use half-toning techniques to convert the “gray scale” mask to a quantized mask, but this will have the undesirable effect of introducing many small shapes, which is not suitable for current mask technology.)
What is needed is a regularization procedure and formulation that can bring a continuous tone mask to a quantized mask that prints similarly well.